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# ice mechanics

By Antonio Lane,2014-08-22 22:58
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ice mechanics

Chapter 1 Introduction

1.1 Ice Crystal

Three types of crystallographic structures presently known of ice.

; the hexagonal structure

; the cubic structure

; the amorphous structure

The hexagonal structure is the only one which is found in nature. Its stable down to very low

temperatures at normal pressure.

Other structures of ice have been observed in the laboratory. At least seven allotropic varieties have been observed pressure exceeding 200 atmospheres. At very low temperature and atmospheric pressure ice of cubic structures and of amorphous form has been identified. It has been known that the oxygen atoms in natural ice are arrange in a tetrahedral pattern, each oxygen atom surrounded by four equally spaced oxygen atoms at the vertex of the tetrahedron as shown if Fig 1.1. If the tetrahedron were perfect the angles between the directions of all oxygen atoms would be which is extremely close to what has been observed of ice. 10928'

The tetrahedral coordination of the oxygen atoms gives rise to a crystal structure present hexagonal symmetry. The hexagonal shape exhibited by many ice crystals is clearly related to the hexagonal symmetry of the molecular arrangement. Another important characteristic of the molecular structure is that the molecular all concentrate close to a series of parallel planes known as the basal planes. The normal to the basal planes is referred to as the c-axis of the crystal. Its

clear that ice has a very open structure and this is reflected in its low density compared to liquid water.

1.2 Ice Nucleation

If we cool a liquid and measure the temperature at which crystallization starts spontaneously, we find that one nucleation temperature always lower than the melting point.

Fig 1.3 shows the cooling curve of pure water when heat is being removed at a constant rate. It may be noticed that a certain amount of suppercooling (SL) is required to nucleate the first ice crystal. The second stage liquid and solid corresponds to crystal growth at the last to the cooling of ice itself.

The condition of supercooling alone is not a sufficient course of a system to begin to the crystallization. Before crystals can grow there must exist in the solution a number of mini centers of crystallization known as seeds, embryos, nuclei. Nucleation may occur spontaneously or it may be induced artificially. It is not always possible, however, to decide whether a system is nucleated of its own or whether it has done so under influence of some external stimulus. We may distinguish the following modes of nucleation:

Heterogeneous nucleation is basically the more important one in nature, either for the formation of

ice crystals in cases the presence of foreign particles significantly reduces the required supercooling below that needed for homogenous nucleation.

1.3 River and Lake Ice

1.3.1 Ice Appearance in Natural Water Bodies

There are essentially three ways in which the first ice may appear in a water body, either in a river, a lake or in the sea. The first one is the heterogeneous nucleation at the surface of a clam or slowly moving water body. The second the nucleation of frazil particles which appear through a fast moving water mass and the last one is simply the freeze up of snow of atmospheric ice nuclei falling into the water.

; Ice nucleation at the surface

The first ice crystals might appear right at the surface of water body in calm water or in laminar flow. Because there will be an important temperature gradient with depth, a thin supercooled water layer will appear at the water-air interface and along the banks of the water body. When the top surface of this supercooled layer will attain the natural temperature of surface nucleation the first ice crystals will appear. Usually this will happen fist along where the water cooling will be faster but ice may also nucleate on the surface away from the banks. Frazil formation is a peculiar phenomenon of ice appearance in river and occasionally in lakes or at sea when surface current induces a turbulent mass and heat exchange.

; Snow-fall

One of the simplest ways to initiate an ice cover on a water body is by secondary nucleation from ice particles coming from the atmosphere, when the water temperature is close to the freezing point. In a lake or a calm water body, heavy snowfall will often initiate the ice cover when the floating snow particles will refreeze at the top exactly at the freezing point during the snowfall. 1.3.2 Static Ice Cover Formation

A static ice cover is one of the forms essentially in plane without ice advection and where the thickening is caused mainly by thermal exchange with the atmosphere.

Bonder ice is usually the first type of ice to appear in a river or along share lines in areas of laminar flow along the water, there is no intermixing of the top layer with the lower ones, the temperature differences are important both in the vertical direction and horizontal away from the banks. The top layer adjacent to the bank goes through sensible supercooling while the average temperature of water the middle of the river may still be far above the freezing point. Ice is then nucleated first along the colder materials of the banks.

; Plate ice

In calm water of lakes, in the sea and in very slow moving water, ice crystals will nucleate right at the water surface in the form of needles. The individual needles will grow in the supercooled top water layer and form a continuous ice plate at the surface. The initial ice plate may also originate from a snow-fall in calm water close to freezing point followed by cold enough weather to

refreeze the snow at the top.

; Growth of Ice

The growth of solid continuous ice in a river or lake from heat exchange with the atmosphere is not as simple as it looks at first sight. If we consider the simple case of vertical static growth of ice from an original ice surface that we take into account the thickness of the existing solid ice sheet and that of a snow layer on the top of the ice and we assume that the temperature at the snow surface is that of the air, we have the basic heat transfer equation.

KdtK()dtisssa gLdhhhs

t(dhds11~ with S()dta~t0dtgLhKhKdt;iss?

Where: P density of solid ice

gacceleration of gravity

coefficient of thermal conduction of ice Ki

average coefficient of thermal conduction of the snow Ks

Llatent heat of fusion of the ice

hthickness of the solid ice sheet at time t

depth of snow hs

Snumber of degree days of frost

and air temperature and temperature of the top surface of the ice as

Its obvious that the above formula will give ice thickness values in excess of what will be found in nature for many reasons. Solar radiation will be absorbed in the ice sheet and they are not included in the heat budget as well as heat adverted at the bottom of from the under going water body. Further more, a boundary layer at the upper snow-air surface makes the surface temperature at this location higher that the air temperature.

But the major difference in nature comes from the fact this is not the way that most static ice covers grow in river and lakes of northern regions. In most cases the weight of snow falls on the ice is adequate to draw the solid ice cover so that water will move through cracks (thermal or others) to flood the ice.

In fact, a rough competition shows that very small amount of deposited snow is sufficient to stop the growth of ice underneath; snow about half the thickness of the ice will suffice. In may areas, a first snowstorm floods the ice of a river or a lake and a new type of ice called snow-ice (whitish in color) begin to form in the water saturated snow layer.

The more usual way of ice cover formation in layer northern rivers in the dynamic accumulation of ice slash and floes to the progression against the flow of the upstream edge of the cover. This process also accounts for some ice cover being pushed along a solid ice edge by the wind and a water current is set up in the epilimnion.

1.4 Sea Ice

1.4.1 Phase Equilibrium in Sea Ice

The composition of sea water from which the ice origin is remarkable uniform in the ocean even if the total concentration of salts varies from one site to the other and decreases appreciably in the deltas of large rivers. The total amount of solids in parts per thousand is usually defined as the salinity of sea water.

The major difference between sea ice and fresh water ice is the amount of salt in the form of concentrated brine pockets, which are squeezed within the ice structure. Because of salt content in

;sea water, the freezing point will be depressed below. Almost at the temperature of 0C

; . 1.80.1~0.2C

1.4.2 Formation of Sea Ice

The appearance of a first ice skin on sea water is very similar to what

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